1. Field of the Invention
The present invention relates to means for calibrating multi-channel imaging systems. In particular, the invention provides an approach for measuring and correcting the field-dependent image distortion, attenuation, and polarization rotation that may be present in multi-channel imaging systems to improve the accuracy of interferometric measurements of optical wavefronts.
2. Description of the Related Art
Multi-channel imaging systems can be used for the measurement of spectroscopic, polarimetric, and/or interferometric properties of objects by simultaneously acquiring a plurality of images on either single or multiple detector arrays. See, for example, U.S. Pat. Nos. 5,926,283, 5,982,497, 4,575,248, 5,589,938, 5,663,793, 5,777,741, 5,883,717, 4,624,569, and 6,304,330. Data from the multiple images can be used for qualitative comparison or can be combined in quantitative ways. In the case of polarimetry and interferometry, the data at each corresponding image pixel are combined through a mathematical algorithm to solve for a desired fundamental optical parameter (e.g., the optical path difference or the polarization state). The registration and losses between images can be extremely important to the accuracy of the calculation.
For ideal imaging systems, the registration between images can be accomplished through simple lateral shifting of the images digitized from the detector arrays. Thus, the registration can be expressed as a simple x and y offset for each image. However, even highly corrected real-world optical systems will contain field-dependent image distortion, which may not be perceptible to the human eye but can cause significant measurement errors. To mitigate these errors, it is first necessary to measure the image distortion and then to construct an algorithm to adjust the images and correct for the distortion. The prior art teaches methods for transforming images into alternate coordinate systems for computer graphics displays, but it is silent with respect to applying these algorithms to multi-channel imaging systems to improve measurement accuracy. See U.S. Pat. No. 6,249,289; L. G. Brown, “A Survey of Image Registration Techniques,” Columbia University, Computer Science Department Publication, New York, N.Y., 1991; and R. C. Gonzalez et al., Digital Image Processing, Addison-Wesley, Reading, Mass., 1987.
Another problem that can greatly affect the accuracy of multi-channel imaging systems is the non-linear detector response between corresponding image pixels. This can be caused by electrically dead pixels on the detector array, non-linear electro-optical response, or obscuration due to contaminants such as dust or coating defects within the optical imaging system. The prior art describes methods for identifying phase-calculation algorithms that are robust with respect to non-linear detector response; however, these algorithms assume the same detector pixel is used for each phase-shifted image (see J. Schmit et al., “Extended averaging technique for derivation of error-compensating algorithms in phase-shifting interferometry,” Applied Optics, Vol. 34, p. 3610, July 1995). The prior art describes methods for calculating data for bad or missing pixels by using nearest neighboring pixels; however, these also assume the same detector pixel is used for each phase-shifted image (see C. K. Hong et al., “Least-squares fitting of the phase map obtained in phase-shifting electronic speckle pattern interferometry,” Optics Letters, Vol. 20, p.931, April 1995). Further, these algorithms reduce spatial resolution. In addition, prior-art methods for calibrating multi-channel interferometer systems describe methods for aligning the optical system to minimize registration errors between images but do not account for geometrical image distortion or pixel dependent non-linearities that may be present in the system, which can significantly limit accuracy. See T. D. Upton et al., “Optical and electronic design of a calibrated multi-channel electronic interferometer for quantitative flow visualization,” Appl. Opt . . . Vol. 34, No. 25, 1995; and C. Koliopoulos et al., “Simultaneous phase shift interferometer,” SPIE Vol. 1531, pp. 119–127, 1991.
Schwider et al. (Applied Optics, Vol. 22, pp. 3421–3432, 1983) and Schmit et. al. (Applied Optics Vol. 34, pp. 3610–3619, 1995) describe the use of extended averaging by introducing a know phase-shift between measurements to eliminate residual phase-dependent systematic error in conventional temporal phase-shifting interferometers. Multi-channel interferometers are typically employed in situations where the relative phase between the test and reference arms is unstable (e.g., due to vibration or turbulence). Therefore, introduction of a precise phase-shift between measurements is not possible, in general, and these methods are not adequate.
Schwider et. al. (Applied Optics, Vol 28, No. 18, pp. 3889–3892, 1989; and Applied Optics, Vol. 38, No. 4, pp. 655–659, 1999) also describe an a posteriori technique for calibrating errors in phase-shifting interferometers. This method requires the introduction of several tilt fringes, fitting the measured data to determine the phase-dependent error and then reprocessing the data to remove the error. In general, this method requires recalibration for every new tilt orientation and does not work for optical alignments near null-fringe condition where interferometers are typically operated to minimize wavefront error. Thus, a general method for the elimination of residual systematic errors in multi-channel interferometer systems is still needed and very desirable.